I don't know why the italics will not turn off--sorry.
This question is especially interesting for me because in other poetry the only consistent difference I can find is that all verse-poetry has line cuts, whether cut by syllable count or by open-form purposes: it does not run from margin to margin. But prose poetry does. So how is it different from, say, many passages of Joyce that are extremely musical but not called "poetry"?
"The Princeton Encyclopedia says the following: A Composition able to have any or all features of the lyric except that it is put on the page--though not conceived of--as prose. It differs from poetic prose in that it is short and compact, from free verse in that it has no line breaks, from a short prose passage in that it has, usually, more pronounced rhythm, sonorous effects, imagery, and a density of expression. It may contain even inner rhyme and metrical runs."
There is a great deal more, and though this does seem to describe "Hysteria," I can't see that it is clearly a way to distinguish. For example, "In Parenthesis" is always called a "poem," but it is 187 pages, not counting the 34 pages of notes, and very little could be called "verse." Some of it has line breaks and some does not. It is often lyrical, and it is extremely imagistic and dense, but so are many passages of what is called "prose" in writers like Joyce, Woolf, Faulkner.
On the other hand, I think the text by Jennifer Militello is just bad writing--purple, whether or not prose, and self absorbed.
So I always end up with students noting all this but acknowledging that the category is not easy to define absolutely. It can explain "Hysteria," but it cannot explain "In Parenthesis," and the latter does not fit into what is called "poetry" in any consistent way.
So I share the interest in any ideas about how to limit the definition.
a starting point for a discussion, maybe

Not that poets have not written prose-poems. Eliot himself wrote 'Hysteria'for instance. In the course of my work on Eliot's early poetry I had an occasion to engage with it and think why it was poetry. You can come up with other instances  from Eliot's contemporaries. But I'm keen to know your opinion on what makes prose poetry. 

As a poet-critic Eliot wrote a lot on poetry and I'd also love to hear what he, or other champions of modernist poetry, thought on the subject.